Arithmetic#

Note

Source: Drawn from the SE4ML Python chapter (chapter_python.rst, lines 196–441) and the C# edition (data/arithmetic.rst). Operator tables, integer vs. float distinction, and math module introduction closely follow the SE4ML presentation.

We start with integers and arithmetic — not because arithmetic is exciting, but because the symbolism should be mostly familiar.

Testing Expressions in the Shell#

Python’s interactive shell is perfect for trying out arithmetic. Start it with python3 and type expressions at the >>> prompt:

>>> 2 + 3
5
>>> 10 - 4
6
>>> 3 * 7
21

The shell evaluates the expression and prints the result immediately. This is much faster than writing a whole program for small experiments.

Numeric Types#

Python has two main numeric types for beginners:

int

Whole numbers, positive or negative, with no fractional part: 0, 42, -17, 1000000.

Python integers have unlimited precision — they can be as large as your computer’s memory allows. There is no overflow.

float

Approximate real numbers, written with a decimal point or an exponent: .2, 2.0, 20., 2000e-1, 2E3.

>>> type(42)
<class 'int'>
>>> type(3.14)
<class 'float'>

Arithmetic Operators#

The arithmetic operators in Python are:

Operator	Meaning	Example
`+`	Addition	`3 + 4` → `7`
`-`	Subtraction	`10 - 3` → `7`
`*`	Multiplication	`3 * 4` → `12`
`/`	Division (always float)	`7 / 2` → `3.5`
`//`	Floor division (integer result)	`7 // 2` → `3`
`%`	Remainder (modulus)	`7 % 2` → `1`
`**`	Exponentiation	`2 ** 10` → `1024`
`-x`	Negation (unary)	`-5`

A key difference from many other languages: / always produces a float, even if both operands are integers:

>>> 7 / 2
3.5
>>> 6 / 2
3.0

Use // when you want a whole-number result:

>>> 7 // 2
3
>>> -7 // 2
-4

Operator Precedence#

Python follows the standard mathematical order of operations. From highest to lowest precedence:

** (exponentiation, right to left)
-x (unary negation)
*, /, //, % (multiplication and division)
+, - (addition and subtraction)

Use parentheses to override the default order:

>>> 2 + 3 * 4
14
>>> (2 + 3) * 4
20

See the appendix for the complete precedence table.

Mixed Arithmetic#

When you mix int and float in an expression, Python converts the int to float automatically:

>>> 1 + 2.0
3.0
>>> type(1 + 2)
<class 'int'>
>>> type(1 + 2.0)
<class 'float'>

This widening conversion preserves the value.

Useful Built-in Functions#

Python provides several useful arithmetic functions built in — no import needed:

Function	Description
`abs(x)`	Absolute value of `x`
`round(x)`	Round to nearest integer
`round(x, n)`	Round to `n` decimal places
`divmod(x, y)`	Returns `(x // y, x % y)` as a tuple
`pow(x, y)`	`x ** y` (also `pow(x, y, z)` for modular exponentiation)
`max(a, b, ...)`	Largest value
`min(a, b, ...)`	Smallest value

>>> abs(-7)
7
>>> round(3.14159, 2)
3.14
>>> divmod(17, 5)
(3, 2)

The math module provides more functions. Import it first:

>>> import math
>>> math.sqrt(2)
1.4142135623730951
>>> math.pi
3.141592653589793
>>> math.floor(3.7)
3
>>> math.ceil(3.2)
4